Flow Of Newtonian And Non-newtonian Fluids With And Without Nano-particles And Damping

This work represents new results regarding some unsteady flows by free convection and heat transfer,and sawtooth pulses like quadratic edges under different circumstances.The corresponding velocity fields,temperature fields,and shear stress have been established analytically by integral transforms like Laplace,Fourier Sine and cosine transforms.In some problems where it was difficult to apply the inverse Laplace transform,an algorithm named as "Stehfest's algorithm" has been used.In Chapter 1,an unsteady flow over infinitely extended vertical plate of nano fluid by free convection and heat transfer has been presented by assuming thermal heat flux.The fractional generalized Fourier's law with Caputo time derivatives with power-law model has been considered to discuss the effects of memory on the behavior of nanofluid.Dimensioless thermal flux,temperature and velocity fields temperature and velocity fields have been obtained analytically by Laplace transformation.Nanofluid is water based having nanoparticles of CuO or Ag.The effects of fractional and physical parameters are discussed graphically.In chapter 2,flow of nanofluid and transferring heat by free convection on a vertical plate with wall slip condition is studied.Generalized Fourier's law has been utilized in order to develop a mathematical model for fractional constitutive equations of thermal flux and shear stress known as the time-fractional Caputo derivative.Analytical solutions for dimensionless temperature and semi analytical for velocity field are obtained by means of integral transform(more exactly by Laplace transform).The velocity field is influenced by both the fluid's temperature and the damping of velocity gradient initiated by fractional derivative.Influences of physical and fractional parameters are presented by graphs.In chapter 3,the natural convection flow of second grade fluid(a type of Differential order fluids)with thermal radiation is considered.The thermal balance equation is fractionalized by generalized Fourier's law.Analytical solution for temperature field and semi analytical for velocity field has been established by Laplace transform.Subsequently,to obtain the inverse Laplace transform of velocity field,Stehfest's algorithm has been applied.Lastly,some graphs have been sketched to discuss the influence of parameters.In chapter 4,an unsteady magnetohydrodynamic(MHD)flow of a generalized Burgers' fluid through two equidistant side walls vertical to the base plate is studied.Flow is started at time t=0+ by the stress(which is supposed to be like sawtooth pulses with quadratic edges)applied on the bottom plate.The solutions calculated by applying the Laplace,and Fourier cosine and sine transformations have been written as a sum of two contributions i.e.Newtonian and non-Newtonian.Finally,graphs have been drawn for different parameters of interest.